shape of constant width 3D (Meissner body)
This 3D Meissner body is a revolution of 2D Reuleaux triangle.
There exists a different shape, the Reuleaux tetrahedron, that is the intersection of four spheres centered at the vertices of a regular tetrahedron. However, that shape is not a 3D shape of constant width.
Also check out shapes of constant width 2D (Reuleaux polygons).